Back in November Anton Geraschenko had an interesting post at the Secret Blogging Seminar based on a preprint by George Bergman. Homological algebra is full of diagram chasing arguments that lead to scary-looking theorems like the Snake Lemma. Bergman claims that these are all special cases of an even-scarier looking but more obvious result he christens the Salamander Lemma. I’ll definitely be looking more closely at this when I get a chance.
“Worm Lemma” would be more like it, because a worm oozes forward in the tube of itself like a sequence oozing from ker to coker, but no point in a snake follows anything like a S-curve, and don’t even get me started about salamanders!
Check out the video of a sidewinder at http://youtube.com/watch?v=JyXNBAHu32o and try to match that with a “natural transformation!”